“[Josh Malina] is Josie’s favorite,” Washington tells PEOPLE. But here’s where things get complicated: “I’m pretty sure [Josh] likes her more than he likes me, and I guarantee if anyone asked him, he would agree.”

The actress’s pup is a major player on the set of the show, which returns for season five in September. “On our first day back with the cast, she was really excited to see some of her favorite people, like Josh Malina,” she says.

It’s clear that celebrity dogs like Josie – who has her own Twitter account – need to be tech-savvy these days. “She’s never been on YouTube I don’t think,” says Washington, “She is a big Instagram star.”